In 2016 Evangelicals debated about the best way to affirm that God is one and yet Father and Son. The old answer is: the Father begets the Son eternally; the Son is eternally begotten. Beget and begotten are old words to describe how fathers generate children. A mother births them; a father begets.
In recent years, evangelicals attempted to find a new way to talk about Father and Son. They said that the Father relates to the Son because he has paternal authority; the Son relates to the Father in a mode of submission. Authority and submission distinguish Father and Son.
For the most part, people found the new approach insufficient. It implied eternal inferiority of the Son, implied two wills, and inserted the human life of Jesus where he obeyed the Father into God. It unintentionally implied a creaturely characteristic in God since Jesus’s creaturely obedience to the Father gets imported into how God is eternally!
Recently, however, a theologian reaffirmed that the Father eternally has authority over the eternally submissive Son. Interestingly, the theologian cited Augustine and Hilary of Poitiers as proponents of his position.
Two reasons why eternal submission does not work
First, Jesus submits to the Father in his role of Mediator, one who became obedient to the point of death in the form of a slave (Phil 2:7). But he was equal to the Father in the form of deity (Phil 2:6).
To transfer submission into God as the way the Father and Son differ is to transfer a creaturely characteristic into God. Because Jesus took on humanity, he obeys the Father vicariously in his role of Mediator for our sake.
Second, the church Fathers such as Augustine and Hilary made the above distinction clearly. They affirmed the obedience of the Son according to his humanity. But they did not pass through this obedience into God to explain how the Son and Father eternally related.
Just one example. Augustine in The Trinity writes: “In the form of a servant which he took he is the Father’s inferior; in the form of God in which he existed even before he took this other he is the Father’s equal.” Elsewhere, he says “the Father is greater than is the form of the servant, whereas the Son is his equal in the form of God.”
This logic undergirds how Augustine and others understand the scriptural passages where Christ submits to the Father or is understood to be less than the Father in some sense.
There is no need to illustrate this point further. It is a patristic commonplace to say that the Son is inferior according to humanity; equal according to divinity. As the Athanasian Creed says, “equal to the Father as regards divinity, less than the Father as regards humanity.” Christ obeyed according to his humanity. He shares one will and equality according to his divinity.
No, it is not Arianism. Arius may have maintained that Christ was divine, but he also affirmed that the Father alone was unoriginate. The Father somehow made the Son by his will to create the cosmos. The implication, however, was clear. This in effect made the Son into a creature, one not sharing the single nature of the one God.
In 357, the so-called Blasphemy of Sirmium (a regional council) described the Son in this way: “And no one is ignorant, that it is catholic doctrine, that there are two persons of Father and Son, and that the Father is greater, and the Son subordinated to the Father together with all things which the Father has subordinated to Him.”
The theologian that I have mentioned does not affirm Arianism. He affirms Nicene notions of Father and Son sharing one essence. Yet he writes: “I believe based on numerous texts that the Son eternally submits to the Father. The duty of submission in the biblical mind does not signal a diminished ontology. It communicates a distinctiveness of person. The Son as Son submits to the Father; the Father as Father is head of the Son.”
In other words, the distinct property of the Son is submission; the distinct property of the Father is headship or authority. That is how we can distinguish persons in the one God. One has authority; one submits.
It is not Arianism, yet such a view still transfers the human obedience of Christ into the nature of God. God by nature has authority and submits in himself, or so the argument goes. But since God has one nature, so one will, that notion internally contracts itself. As William Perkins, the father of Puritanism, says, “because as they are all one in nature, so are they all one in will.” Hence, “[T]he decree of the Father is the decree of the Son and the Holy Ghost.”
One decree. One will. There is not a decree from the authoritative one and submission among the submissive one. One will means God is not divided. It means that Jesus’s genuine human will obeys God in all things for our sake. But his divine will is the one will of God always. There is no sense in which the one God can submit to himself—at least in any way like we can conceive of it. Jesus submits to the Father.
Transferring human obedience, creaturely obedience, into the life of God implies his creaturehood. That implication must be rejected. As the Bible tells us and consent of the church has confirmed, the Father and Son are distinguished by Fatherness and Sonness. Their relation is one of Fatherness and Sonness.
That’s about it. It is a mystery, one which we breach when we import human categories into God.
 See The Trinity, trans. Edmund Hill, ed. John E. Rotelle, 2nd ed. (New York: New City Press, 1991), 77, 78.
 Although I might want to show how Hilary rejected the Arian idea that Father and Son unite around a relation of will. He denies that because the Father and Son relate by eternal generation. Like Augustine too, Hilary affirms, “The obedience unto death is not in the form of God, just as the form of God is not in the form of a slave” (The Trinity 9.14).